The Roar unleashed 30 shots to six in Saturday's match on a patchy Suncorp Stadium deck, but in the end all they needed was Florin Berenguer's 58th-minute strike.
It marked Brisbane's first clean sheet since April 20, 2024, when they fought out a 0-0 draw with Melbourne Victory.
More importantly, the Roar's fourth win of the campaign has moved them four points ahead of last-placed Perth.
The Glory will need to win their last two games - against Auckland FC and the Phoenix in New Zealand - to have any chance of leapfrogging Brisbane.
The Roar round out their season away to Central Coast next Friday night.
Wellington remain in 11th spot, six points ahead of Brisbane.
Saturday's win was just reward for Roar goalkeeper Matt Acton in his 50th ALM match.
"It's great to get a result and a clean sheet for our fans," Brisbane coach Ruben Zadkovich said.
"It's been very evident and clear how together the group is and how much the older ones are getting around the younger ones.
"I'm extremely proud at the moment."
The Roar fired off 13 shots to two and enjoyed 61 per cent possession in a dominant first-half display, but they were unable to break through Wellington's defence.
Emerging Brisbane star Sam Klein fired the first warning shot, with his 30-yard thunderbolt crashing into the upright and bouncing away.
Roar captain Jay O'Shea had two promising chances from free kicks - one that flew just wide, and the other that was palmed away from Phoenix goalkeeper Josh Oluwayemi.
Brisbane finally broke through for a goal early in the second half when a backheel from import Asumah Abubakar opened the door for Berenguer.
The Frenchman made no mistake, controlling the ball with his thigh before unleashing a volley from outside the box to send the home fans wild.
Wellington had barely fired a shot until that moment, but they sprang to life after making a triple substitution in the 63rd minute, with Paulo Retre, Luke Brooke-Smith and Nathan Walker brought on.
Walker unleashed a shot two minutes later that forced a sharp save from Acton.
And Acton was forced into another sharp save in the 67th minute when Corban Piper unleashed from the near post.
Acton's saves ensured he posted just the sixth clean sheet of his 50-game ALM career.
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